名 here is a verb meaning 'to possess' (a Classical Chinese sense, as in 一无所有 lacking everything). 文 is an old copper coin. So literally 'not possessing one cash.' Synonym 一文不名 (yīwénbùmíng) reverses the order — interchangeable.
mistakes
Don't read 名 as 'name' here — that's a learner trap. 不名一文 ≠ 'no one knows my name.' It's about money.
